Number of solutions in a box of a linear equation in an Abelian group

• Autorzy: Maciej Zakarczemny
• Języki publikacji: EN

Abstrakty

EN

For every finite Abelian group Γ and for all $g,a₁,..., a_{k} ∈ Γ$, if there exists a solution of the equation $∑_{i=1}^{k} a_{i}x_{i} = g$ in non-negative integers $x_{i} ≤ b_{i}$, where $b_{i}$ are positive integers, then the number of such solutions is estimated from below in the best possible way.

Kategorie tematyczne

• 11D79: Congruences in many variables
• 20K01: Finite abelian groups [For sumsets, see and ]

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 143
• Numer: 1
• Strony: 17-22

Daty

wydano

2016

Twórcy

autor

Maciej Zakarczemny

• Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland

Identyfikatory

DOI

10.4064/cm6145-12-2015